we have that
the center C at (-2,5) and point M (6,-1) on the circumference of the circle
we know that
the radius of the circle is equal to the distance between the center and point M
step 1
find the distance CM
d=√[(y2-y1)²+(x2-x1)²]-----> d=√[(-1-5)²+(6+2)²]----> d=√[36+64]
d=√100-----> d=10 units
the radius r=10 units
so
the diameter=2*r----> 2*10----> 20 units
the answer is
diameter of the circle is 20 units
the equation of the circle is
(x+2)²+(y-5)²=10²
see the attached figure
